Math 443 Algebraic topology.
Fall,
2020.
Lecture notes and recordings.
This page will
give handwritten notes for each lecture as the semester progresses. It is
written in reverse chronological order, so you see the most recent
notes first. However this means that helpful links appear when a
topic is first mentioned chronologically, meaning the last time
it appears below.
Here are the
lecture notes from Fall 2019 and from previous years by recursion.
December 9, 2020. Review for final exam. Lecture notes Zoom video Zoom audio
December 7, 2020. Vector bundles, induced bundles and classifying spaces. Lecture notes Zoom video Zoom audio
December 2, 2020. The Hairy Ball Theorem video. More Hopf invariant, vector fields and vector bundles. Lecture notes The recording began a few minutes late. Zoom video Zoom audio
November 30, 2020. Cup products and the Hopf invariant. Lecture notes Zoom video Zoom audio
November 23, 2020. Wikipedia article on Platonic solids. The Euler characteristic and Platonic solids. Lecture notes Zoom video Zoom audio
November 18, 2020. Eilenberg-Mac Lane spaces. Lecture notes Zoom video Zoom audio
November 16, 2020. The homology of projective spaces and related topics. Lecture notes Zoom video Zoom audio
November 11, 2020. Ramanujan video. Trailer for "The Man Who Knew Infinity". Ramanujan Pi formula. The classifying space of a group G and G-CW complexes. Lecture notes Zoom video Zoom audio
November 9, 2020. CW-complexes and simplicial sets. Discussion of simplicial sets in ESHT book, page 242. Lecture notes Zoom video Zoom audio
November 4, 2020. CW-complexes and Cartesian products. Lecture notes Zoom video Zoom audio
November 2, 2020. The universal coefficient theorem. Lecture notes Zoom video Zoom audio
October 28, 2020. More homological algebra. Lecture notes. No recording available.
October 26, 2020. Homological algebra. Lecture notes Zoom video Zoom audio
October 21, 2020. Proving the excision axiom. Lecture notes Zoom
video part a Zoom
audio part a
Zoom video part b Zoom
audio part b
October 19, 2020. Benoit Mandelbort page including video link. Proving the homotopy axiom. Lecture notes Zoom audio Zoom video
October 14, 2020. Consequences of the Eilenberg-Steenrod axioms. Lecture notes Zoom audio Zoom video
October 12, 2020. Toward the singular chain complex of a topological space. Lecture notes Zoom audio Zoom video
October 7, 2020. Homology and exactness. Lecture notes Zoom audio Zoom video
October 5, 2020. More about the universal cover. Lecture notes Zoom audio Zoom video
September 30, 2020. Covering spaces and the universal cover. A Beautiful Mind). Lecture notes Zoom audio Zoom video
September 28, 2020. More about the van Kampen theorem. Octagon genus 2 video. Lecture notes Zoom audio Zoom video
September 23, 2020. More applications of the fundamental group of the circle and the van Kampen theorem. Fermat's last theorem page Lecture notes Zoom audio Zoom video
September 21, 2020. The fundamental group of the circle with applications. Lecture notes Zoom audio Zoom video
September 16, 2020. The Hopf maps and higher homotopy groups. Hopf fibration page with link to Niles Johnson's video. Lecture notes Zoom audio Zoom video
September 14, 2020. More category theory. Lecture notes Zoom audio Zoom video
September 9, 2020. Introduction to category theory. Archimedes palimpsest page Lecture notes Zoom audio Zoom video
September 2, 2020. More about the fundamental group. Archimedes page Lecture notes Zoom audio Zoom video
August 31, 2020. More about the fundamental group. Pi Day videos 1 and 2. Lecture notes Zoom audio Zoom video
August 26, 2020. Understanding the coffee cup and belt tricks. Two videos: one two. Lecture notes Zoom audio Zoom video